The word death in the Bible actually has more than one sense. When we think of death, it is usually the cessation of something. But the Bible does not speak of death in those kinds of terms. Death in scripture actually refers to a separation, and has two primary uses.

Physical Death...

Physical death is the separation of the soul (or spirit) from the body. James wrote, "For as the body without the spirit is dead, so faith without works is dead also." (Jms 2:26) Solomon wrote, "Then the dust will return to the earth as it was, And the spirit will return to God who gave it." (Eccl 12:7) These two passages give us an accurate picture of when death occurs. I have seen people die. But I only saw the heart stop beating and their breathing stop. I only saw the symptoms of the spirit leaving the body.

Spiritual Death...

Spiritual death is the separation of the individual from God's fellowship and blessings. God told Adam, "but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die." (Gen 2:17) He did not die physically on the day he ate it, for he went on to have a family and live 930 years. But he was expelled from the garden, and from the presence of God. Isaiah wrote, "But your iniquities have separated you from your God; And your sins have hidden His face from you, So that He will not hear." (Isa 59:2) To die physically while separated from God dooms one to an eternity away from Him.

This is the death that Jesus came to save us from. "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord." (Rom 6:23) The death and the life in this passage are both spiritual in nature. The life we live upon this earth will determine our eternal fate, and Jesus will be the judge (Mt 7:21-23). Only through Jesus will we find our way back to God's blessings and fellowship (Acts 4:12).